Abstract
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.
Highlights
The first part of this paper deals with a systematic analysis of the supersymmetric values that certain supermultiplets can take, but in the context of local supersymmetry which is somewhat more subtle
To explain the strategy that we will follow in this paper for establishing supersymmetric backgrounds and to further elucidate some of the conceptual issues, we start in section 2 by discussing a single N = 2 vector supermultiplet coupled to a conformal supergravity background
When deriving the consequences of supersymmetry for the resulting field configuration we naturally discover that the conformal supergravity background itself is subject to constraints
Summary
We derive the conditions that follow from imposing full supersymmetry on a field configuration consisting of a single vector supermultiplet in a conformal supergravity background. Continuing this analysis will show that this multiplet is restricted to a constant, or, equivalently, that in the supersymmetric limit the two multiplets must be proportional to one another This is an example of a more generic result: if the lowestweight (scalar) component of a multiplet does not transform under dilatations and U(1) transformations, the supersymmetry algebra implies that the lowest-weight fermion into which it transforms must be invariant under S-supersymmetry. To avoid confusion we will usually write the conformal gauge connection fμa explicitly in the purely bosonic expressions and not keep it implicit as we do when dealing with supercovariant derivatives In this strategy the initial vector multiplet plays a key role, but in due course we will demonstrate that the results will be independent of the choice of the particular supermultiplet from where one starts this procedure.
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